Can't help you directly much.
No 30 amp plug isn't a big deal. Get a thick/heavy gauge 15 amp extension cord, keep the make end, cut off the female end and put a plug on that matches your trailer inlet. Problem solved.
I have a Yamaha 2400 and run a 13.5k air with it without any issues. Couple things if you haven't found in searches yet: may be able to get a soft start kit to install in the ac to help. I have heard of people running 13.5k units on a Honda 2000 with a soft start, but most people will say it's not possible. Some people limp through by starting the fan first (low high switch) then moving the thermostat to start the cooling. Breaks up the surge a bit. I have even seen kids that will delay the compressor start for a number of seconds after a call for cooling.
In the end, buying an undersized generator can be a persistent pain in the arse. Best thing I could suggest would be to buy from a business with a liberal return policy and test the small one out.